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Simplifying h2 + -24h + 47 = 2 Reorder the terms: 47 + -24h + h2 = 2 Solving 47 + -24h + h2 = 2 Solving for variable 'h'. Reorder the terms: 47 + -2 + -24h + h2 = 2 + -2 Combine like terms: 47 + -2 = 45 45 + -24h + h2 = 2 + -2 Combine like terms: 2 + -2 = 0 45 + -24h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -24h + -45 + h2 = 0 + -45 Reorder the terms: 45 + -45 + -24h + h2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -24h + h2 = 0 + -45 -24h + h2 = 0 + -45 Combine like terms: 0 + -45 = -45 -24h + h2 = -45 The h term is -24h. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24h + 144 + h2 = -45 + 144 Reorder the terms: 144 + -24h + h2 = -45 + 144 Combine like terms: -45 + 144 = 99 144 + -24h + h2 = 99 Factor a perfect square on the left side: (h + -12)(h + -12) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (h + -12) equal to 9.949874371 and -9.949874371.Subproblem 1
h + -12 = 9.949874371 Simplifying h + -12 = 9.949874371 Reorder the terms: -12 + h = 9.949874371 Solving -12 + h = 9.949874371 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + h = 9.949874371 + 12 Combine like terms: -12 + 12 = 0 0 + h = 9.949874371 + 12 h = 9.949874371 + 12 Combine like terms: 9.949874371 + 12 = 21.949874371 h = 21.949874371 Simplifying h = 21.949874371Subproblem 2
h + -12 = -9.949874371 Simplifying h + -12 = -9.949874371 Reorder the terms: -12 + h = -9.949874371 Solving -12 + h = -9.949874371 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + h = -9.949874371 + 12 Combine like terms: -12 + 12 = 0 0 + h = -9.949874371 + 12 h = -9.949874371 + 12 Combine like terms: -9.949874371 + 12 = 2.050125629 h = 2.050125629 Simplifying h = 2.050125629Solution
The solution to the problem is based on the solutions from the subproblems. h = {21.949874371, 2.050125629}
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